English

Three lectures on classical integrable systems and gauge field theories

High Energy Physics - Theory 2009-11-13 v1

Abstract

In these lectures I consider the Hitchin integrable systems and their relations with the self-duality equations and the twisted super-symmetric Yang-Mills theory in four dimension follow Hitchin and Kapustin-Witten. I define the Symplectic Hecke correspondence between different integrable systems. As an example I consider Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL(N,C) and explain the Symplectic Hecke correspondence for these systems.

Keywords

Cite

@article{arxiv.0802.3857,
  title  = {Three lectures on classical integrable systems and gauge field theories},
  author = {M. Olshanetsky},
  journal= {arXiv preprint arXiv:0802.3857},
  year   = {2009}
}

Comments

36 pages, Lectures given at Advanced Summer School on Integrable Systems and Quantum Symmetries (Prague, June, 2007)

R2 v1 2026-06-21T10:16:06.247Z